Asymptotic Expansions Of Extremes From General Error Distribution

For a sequence of independent and identically distributed random variables with marginal general error distribution, with optimal normalizing constants, the asymp-totic expansions of distributions and moments of the normalized partial maxima are studied, which consist of the contents of this thesis.For the first part of this thesis, by deriving its Mills ratio, we deduce its distribu-tional tail representation and the optimal normalizing constants. Furthermore, with optimal normalizing constants, the higher-order asymptotic expansions for distribu-tions of normalized partial maximum from the general error distribution is derived through the expanded distributional tail representation, by which one deduces its as-sociated convergence rate of the distribution of the extreme to the Gumbel extreme value distribution.In the second part, based on the asymptotic expansions for distributions of extremes, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution.